Answer:
![T_( - 5 ,</p><p>8) \: or \: D'(x,y) →D(x - 5,y + 8)](https://img.qammunity.org/2021/formulas/mathematics/middle-school/76kilapydo5zu2tss73k2snvi7cp1jgo2e.png)
Explanation:
![T _ { ? ,</p><p>?}](https://img.qammunity.org/2021/formulas/mathematics/middle-school/lpt94kihoeejjci0p3k79wxh47hj8v97cd.png)
![D'(x,y) →D(x \pm ?,y \pm ?)](https://img.qammunity.org/2021/formulas/mathematics/middle-school/9bz85nohzbd7avam1y31rks9lgxxft3asd.png)
given D : (7,-3), and D' : (2,5)
the coordinates of D can be represented as (x1,y1), and the coordinates of D' can be represented as (x,y).
you can simply take the difference in the x values and difference in the y values from the preimage to image.
like this:
f'(x,y) → f(x+(x-x1),y+(y-y1)) :
![</p><p>T _ {(x-x_1),(y-y_1)}](https://img.qammunity.org/2021/formulas/mathematics/middle-school/a3q9amntvhypd5yaoamnn7twjt9x245coq.png)
D'(x,y) → D(x+(2-7),y+(5--3))
D'(x,y) → D(x-5,y+8) :
![</p><p>T _ {-5 ,8}](https://img.qammunity.org/2021/formulas/mathematics/middle-school/h77ksbthiwebqhcgmxamw68ifle3scjf3b.png)